On the Asymptotic Consistency of Minimum Divergence and Least-Squares Principles

Euclidean distance is a discrepancy measure between two real-valued functions. Divergence is a discrepancy measure between two positive functions. Corresponding to these two well-known discrepancy measures, there are two inference principles; namely, the least-squares principle for choosing a real-valued function subject to linear constraints, and the minimum-divergence principle for choosing a positive function subject to linear constraints. To make the connection between these two principles more transparent, this correspondence provides an observation and a constructive proof that the minimum-divergence principle reduces to the least-squares principle asymptotically as the positivity requirements are de-emphasized. Hence, these two principles are asymptotically consistent.